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ContinuedFraction (Commons Math 3.2 API)
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org.apache.commons.math3.util</FONT>
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Class ContinuedFraction</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.util.ContinuedFraction</B>
</PRE>
<HR>
<DL>
<DT><PRE>public abstract class <B>ContinuedFraction</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
Provides a generic means to evaluate continued fractions.  Subclasses simply
 provided the a and b coefficients to evaluate the continued fraction.

 <p>
 References:
 <ul>
 <li><a href="http://mathworld.wolfram.com/ContinuedFraction.html">
 Continued Fraction</a></li>
 </ul>
 </p>
<P>

<P>
<DL>
<DT><B>Version:</B></DT>
  <DD>$Id: ContinuedFraction.java 1416643 2012-12-03 19:37:14Z tn $</DD>
</DL>
<HR>

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<CODE>protected </CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#ContinuedFraction()">ContinuedFraction</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Default constructor.</TD>
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<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#evaluate(double)">evaluate</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Evaluates the continued fraction at the value x.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#evaluate(double, double)">evaluate</A></B>(double&nbsp;x,
         double&nbsp;epsilon)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Evaluates the continued fraction at the value x.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#evaluate(double, double, int)">evaluate</A></B>(double&nbsp;x,
         double&nbsp;epsilon,
         int&nbsp;maxIterations)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Evaluates the continued fraction at the value x.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#evaluate(double, int)">evaluate</A></B>(double&nbsp;x,
         int&nbsp;maxIterations)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Evaluates the continued fraction at the value x.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected abstract &nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#getA(int, double)">getA</A></B>(int&nbsp;n,
     double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Access the n-th a coefficient of the continued fraction.</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected abstract &nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/util/ContinuedFraction.html#getB(int, double)">getB</A></B>(int&nbsp;n,
     double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Access the n-th b coefficient of the continued fraction.</TD>
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<A NAME="ContinuedFraction()"><!-- --></A><H3>
ContinuedFraction</H3>
<PRE>
protected <B>ContinuedFraction</B>()</PRE>
<DL>
<DD>Default constructor.
<P>
</DL>

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<A NAME="getA(int, double)"><!-- --></A><H3>
getA</H3>
<PRE>
protected abstract double <B>getA</B>(int&nbsp;n,
                               double&nbsp;x)</PRE>
<DL>
<DD>Access the n-th a coefficient of the continued fraction.  Since a can be
 a function of the evaluation point, x, that is passed in as well.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>n</CODE> - the coefficient index to retrieve.<DD><CODE>x</CODE> - the evaluation point.
<DT><B>Returns:</B><DD>the n-th a coefficient.</DL>
</DD>
</DL>
<HR>

<A NAME="getB(int, double)"><!-- --></A><H3>
getB</H3>
<PRE>
protected abstract double <B>getB</B>(int&nbsp;n,
                               double&nbsp;x)</PRE>
<DL>
<DD>Access the n-th b coefficient of the continued fraction.  Since b can be
 a function of the evaluation point, x, that is passed in as well.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>n</CODE> - the coefficient index to retrieve.<DD><CODE>x</CODE> - the evaluation point.
<DT><B>Returns:</B><DD>the n-th b coefficient.</DL>
</DD>
</DL>
<HR>

<A NAME="evaluate(double)"><!-- --></A><H3>
evaluate</H3>
<PRE>
public double <B>evaluate</B>(double&nbsp;x)
                throws <A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></PRE>
<DL>
<DD>Evaluates the continued fraction at the value x.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the evaluation point.
<DT><B>Returns:</B><DD>the value of the continued fraction evaluated at x.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the algorithm fails to converge.</DL>
</DD>
</DL>
<HR>

<A NAME="evaluate(double, double)"><!-- --></A><H3>
evaluate</H3>
<PRE>
public double <B>evaluate</B>(double&nbsp;x,
                       double&nbsp;epsilon)
                throws <A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></PRE>
<DL>
<DD>Evaluates the continued fraction at the value x.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the evaluation point.<DD><CODE>epsilon</CODE> - maximum error allowed.
<DT><B>Returns:</B><DD>the value of the continued fraction evaluated at x.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the algorithm fails to converge.</DL>
</DD>
</DL>
<HR>

<A NAME="evaluate(double, int)"><!-- --></A><H3>
evaluate</H3>
<PRE>
public double <B>evaluate</B>(double&nbsp;x,
                       int&nbsp;maxIterations)
                throws <A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A>,
                       <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Evaluates the continued fraction at the value x.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the evaluation point.<DD><CODE>maxIterations</CODE> - maximum number of convergents
<DT><B>Returns:</B><DD>the value of the continued fraction evaluated at x.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the algorithm fails to converge.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if maximal number of iterations is reached</DL>
</DD>
</DL>
<HR>

<A NAME="evaluate(double, double, int)"><!-- --></A><H3>
evaluate</H3>
<PRE>
public double <B>evaluate</B>(double&nbsp;x,
                       double&nbsp;epsilon,
                       int&nbsp;maxIterations)
                throws <A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A>,
                       <A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></PRE>
<DL>
<DD>Evaluates the continued fraction at the value x.
 <p>
 The implementation of this method is based on the modified Lentz algorithm as described
 on page 18 ff. in:
 <ul>
   <li>
   I. J. Thompson,  A. R. Barnett. "Coulomb and Bessel Functions of Complex Arguments and Order."
   <a target="_blank" href="http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf">
   http://www.fresco.org.uk/papers/Thompson-JCP64p490.pdf</a>
   </li>
 </ul>
 <b>Note:</b> the implementation uses the terms a<sub>i</sub> and b<sub>i</sub> as defined in
 <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction @ MathWorld</a>.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the evaluation point.<DD><CODE>epsilon</CODE> - maximum error allowed.<DD><CODE>maxIterations</CODE> - maximum number of convergents
<DT><B>Returns:</B><DD>the value of the continued fraction evaluated at x.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/ConvergenceException.html" title="class in org.apache.commons.math3.exception">ConvergenceException</A></CODE> - if the algorithm fails to converge.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if maximal number of iterations is reached</DL>
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